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X₁₂₄₅¶

ISOGONAL CONJUGATE OF X₁₀₁₀

X₁₂₄₅ is the isogonal conjugate of X₁₀₁₀.

X₁₂₄₅ (ISOGONAL CONJUGATE OF X₁₀₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1245 = ISOGONAL CONJUGATE OF X_1010."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01245(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1245 = ISOGONAL CONJUGATE OF X_1010 on reference triangle ABC."""
            X_1010 = eval_trilinear_point(model, A, B, C, '(b*c*(a**(2) + (b + c)**(2))/(b + c))', ID="X_1010", classes=["center"])
            X_1245 = isogonal_conjugate(model, A, B, C, X_1010, ID="X_1245", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            central_line(model, X_3, X_31, 3, 31, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_1, X_69, 1, 69, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_42, X_72, 42, 72, incident=True)
            return promote_point_to_top(model, X_1245)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_1245 on the given reference triangle."""
            model = create_model('X_1245 = ISOGONAL CONJUGATE OF X_1010')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01245(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-01245.json"))
            write_center_svg(
                model_acute,
                here / "x-01245.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1245¶

X₁₂₄₅¶